The quenched chiral logarithms are examined on a 16(3)x28 lattice with Iwasaki gauge action and overlap fermions. The pion decay constant f(pi) is used to set the lattice spacing, a=0.200(3) fm. With pion mass as low as similar to180 MeV, we see the quenched chiral logarithms clearly in m(pi)(2)/m and f(P), the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory (chiPT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral logarithmic parameter delta together with other low-energy parameters. Only for m(pi)less than or equal to300 MeV do we obtain a consistent and stable fit with a constant delta which we determine to be 0.24(3)(4) (at the chiral scale Lambda(chi)=0.8 GeV). By comparing to the 12(3)x28 lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to m(pi)similar to500-600 MeV. The scale independent delta is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient C-1/2 in the nucleon mass is consistent with the prediction of one-loop chiPT. We also obtain the low energy constant L-5 from f(pi). We conclude from this study that it is imperative to cover only the range of data with the pion mass less than similar to300 MeV in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop chiPT.